Calculus 2 Past Exam Question

[alpine peak]

I really don't know how to approach this one :(

[midnight osprey]

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[left oar]

u-substitution is the way to go

I'll let you try to choose u yourself, unless you're really stuck

[alpine peak]

trying it right now but I just don't see it

[left oar]

I used 1+sqrtx for u

that way the sqrt in the denominator gets canceled out by du or whatever

I can send you my solution if you'd like

[alpine peak]

yes please

like i just don't know where to put the 1/2 sqr(x)

[left oar]

Excuse handwriting plus like using D and E for constants

I think you just made the mistake that you have to flip the 1/2 sqrtx

[alpine peak]

nah, I plain up forgot that u can actually use the du equality itself to simplify the thing

i don't know why but I always feel like it needs to be simplified enough before even putting the du form

rip

Thanks a lot

[left oar]

No problem, glad I could help

[alpine peak]

Can I ask one more thing?

I keep finding -1 for this one but chatgpt keeps telling me a different answer everytime

[left oar]

Sure

[alpine peak]

I used integration by parts first then simply calculated the limit to infinity

seems like a very simple one, I don't know why chatgpt is having so much trouble

[left oar]

I wouldn't trust chat gpts ability with any form of math just based on how it works like its a language model or whatever its called like it predicts text

[alpine peak]

ik but TAs aren't really helpful either and the teacher takes 3-4 days to reply to a simple query :D

[left oar]

Like if it gets something right its not because it was right but rather that it happened to be righr that time

Try wolfram alpha

If you havent

[alpine peak]

i use it for showing the process

[left oar]

But how can you be sure that it even gets the process right?

[alpine peak]

I check/compare with my book but yeah i get your point

wolfram alpha asks for a pro license tho

Does it work with statistic questions as well? Because that's where I really need the help

[left oar]

Thats fair

And yeah the licence thing sucks

Idk I have free and just try to cope

I don't know about statistics though

[alpine peak]

ok found the issue, i have no idea why f*g is a limit with those bracket thingies that indicates you can just fill it in now

[left oar]

Because like primitive function or whatever when you put in the values

So it shows that the next step will be F(b) - F(a) so to speak with the limit infront

Im using this notation cause thats the first you learn with normal integrals like integral from a to b etc

Sorry I'm not really making sense

My reasoning might be very wrong idk at this point

[alpine peak]

Checked my integration by parts notes, the book and googled it a little still couldn't find anything

will make an another post and ask it there

thanks anyways

[alpine peak]

+close